We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametric-window moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.

This post contains a list of the AI-related seminars that are scheduled to take place between 3 October and 30 November 2025. All events detailed here are free and open for anyone to attend virtually. Daniel Kuhn (EPFL) Association of European Operational Research Societies To receive the seminar link, sign up to the mailing list . Chia-Lin Wei (University of Washington) University of Michigan Medical School The seminar will be live-streamed on the DCMB YouTube Channel . Jannis Kurtz (University of Amsterdam) Association of European Operational Research Societies To receive the seminar link, sign up to the mailing list .

The UK's most scenic train routes revealed - and tickets start from just £4.20 Do YOU want to work from a sun lounger? It's never too late to book - a great holiday is just around the corner! Here's our edit of the best last-minute holiday destinations that everyone will LOVE The beloved Dorset hotel'in disrepair' set to finally make a comeback My night inside the world's biggest capsule hotel where stays start from just £30 Terrifying swing throws you through the air at 131ft in Scotland - would YOU pay £90 for it? Woman shares'genius' packing hacks that can save time and hassle on your next trip The Wetherspoons hotel that's been named one of the UK's best pubs - and it's on the beach The'indulgent' Christmas Day brunch at a London luxury hotel is returning - here's how much it will cost Where to find the 26-mile railway that changed train travel forever - and it's right here in the UK Why the'most beautiful country you've never heard of' in Central Asia should be next on your list Inside the world's smallest'divided island' - and how a lighthouse forced the borders to change Airline launches new holiday routes from the UK - including'Greece's best-kept secret' The UK's most historic holiday home revealed - and it's a former jail cell A futuristic £14.5million plane with TV screens instead of windows has been unveiled. The jet, called Phantom 3500, will use technology on the outside of the plane to provide immersive views.

Neural Information Processing Systems http://nips.cc/

Musk becomes world's first half-trillionaire Tesla boss Elon Musk has become the first person ever to achieve a net worth of more than $500bn (£370.9bn), The tech magnate's net worth briefly reached $500.1bn on Wednesday afternoon New York time, before dipping slightly to just over $499bn later in the day, the Forbes billionaires index reported. Alongside Tesla, valuations of his other ventures, including the artificial intelligence start-up xAI and rocket company SpaceX, have also reportedly climbed in recent months. According to Forbes' billionaires index, Oracle founder Larry Ellison is the world's second richest person, with a fortune of about $350.7bn. Mr Ellison briefly overtook Musk last month after shares in Oracle soared by more than 40%, boosted by the firm's surprisingly rosy outlook for its cloud infrastructure business and artificial intelligence (AI) deals.

A data-driven approach, however, could overcome limitations in such rule-based approaches and improve precision mappings for individuals.

Neural Information Processing Systems http://nips.cc/

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains understudied. As a result, existing implementations often resort to conservative hyperparameter choices to ensure stability, which requires more training samples and increases computational costs. Hence, developing models for reliably tracking the underlying optimization dynamics and leveraging them into training enables more sample-efficient regimes and further unleashes scalable post-training. We address this gap by formalizing the stochastic optimization problem of policy gradients with explicit consideration of second-order geometry. We propose a tractable computational framework that tracks and leverages curvature information during policy updates. We further employ this framework to design interventions in the optimization process through data selection. The resultant algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out. Theoretically, we establish monotonic improvement guarantees under realistic assumptions. On standard math reasoning benchmarks, we empirically show that CAPO ensures stable updates under aggressive learning regimes where baselines catastrophically fail. With minimal intervention (rejecting fewer than 8% of tokens), CAPO achieves up to 30x improvement in sample efficiency over standard GRPO for LLM reasoning.

We introduce a novel version of the geometric scattering transform for geometric graphs containing scalar and vector node features. This new scattering transform has desirable symmetries with respect to rigid-body roto-translations (i.e., $SE(3)$-equivariance) and may be incorporated into a geometric GNN framework. We empirically show that our equivariant scattering-based GNN achieves comparable performance to other equivariant message-passing-based GNNs at a fraction of the parameter count.

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.